What is the simplified value of left[frac{lef | vedclass

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(D) Given expression: $\left[\frac{\sec ^{3} x-	an ^{3} x}{\sec x-	an x}ight]-2 	an ^{2} x-\sec x 	an x$
Using the algebraic identity $a^3 - b^

Vedclass · Accepted Answer

$1$

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(D) Given expression: $\left[\frac{\sec ^{3} x-	an ^{3} x}{\sec x-	an x}ight]-2 	an ^{2} x-\sec x 	an x$
Using the algebraic identity $a^3 - b^3 = (a - b)(a^2 + b^2 + ab)$,where $a = \sec x$ and $b = 	an x$:
$= \frac{(\sec x - 	an x)(\sec^2 x + 	an^2 x + \sec x 	an x)}{\sec x - 	an x} - 2 	an^2 x - \sec x 	an x$
$= (\sec^2 x + 	an^2 x + \sec x 	an x) - 2 	an^2 x - \sec x 	an x$
$= \sec^2 x + 	an^2 x - 2 	an^2 x + \sec x 	an x - \sec x 	an x$
$= \sec^2 x - 	an^2 x$
Using the trigonometric identity $\sec^2 x - 	an^2 x = 1$,the simplified value is $1$.

What is the simplified value of $\left[\frac{\left(\sec ^{3} x-\tan ^{3} x\right)}{(\sec x-\tan x)}\right]-2 \tan ^{2} x-\sec x \tan x ?$

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